PoojaMoolya at 10:08, 10 October 2019

2019-10-10T10:08:11Z

PoojaMoolya: Created page with "{| border = 1 || ''' Time''' || ''' Narration''' |- |00:01 |Welcome to the spoken tutorial on '''Theorems in GeoGebra'''. |- |00:06 |In this tutorial we will state and pr..."

2019-10-10T09:52:52Z

Created page with "{| border = 1 || ''' Time''' || ''' Narration''' |- |00:01 |Welcome to the spoken tutorial on '''Theorems in GeoGebra'''. |- |00:06 |In this tutorial we will state and pr..."

New page

{| border = 1
|| ''' Time'''
|| ''' Narration'''

|-
|00:01
|Welcome to the spoken tutorial on '''Theorems in GeoGebra'''.

|-
|00:06
|In this tutorial we will state and prove,

'''Pythagoras''' theorem and

Midpoint theorem using '''Geogebra''' .

|-
|00:16
| To record this tutorial, I am using;

'''Ubuntu Linux''' OS version 16.04

'''GeoGebra''' version 5.0438.0-d.

|-
|00:29
| To follow this tutorial, learner should be familiar with '''GeoGebra interface'''.

For the prerequisite '''GeoGebra''' tutorials, please visit this website.

|-
|00:40
|Let us state the '''Pythagoras '''theorem.

|-
|00:43
|The square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.

|-
| 00:50
| I have already opened the '''GeoGebra interface'''.

|-
|00:54
| We will begin with the drawing of a semicircle.

|-
|00:58
| Click on the '''Semicircle through 2 Points '''tool.

|-
|01:02
|Then click to mark two points in the '''Graphics view'''.

|-
|01:07
|Using the '''Point''' we will mark another point '''C''' on the semicircle '''c'''.

|-
|01:14
| Now let us draw a triangle '''ABC''' using the points on the semicircle.

|-
|01:19
|Click on the '''Polygon''' tool and draw triangle '''ABC'''

|-
|01:26
|Here we are using semicircle to draw the triangle.

|-
|01:30
|This is because we need the measure of one angle to be 90 degree.

|-
|01:36
| Let us measure the angles of the triangle.

|-
|01:39
|Click on the '''Angle''' tool and click inside the triangle. Here angle '''ACB''' is 90 degrees.

|-
|01:49
| Now we will hide the semicircle c.

|-
|01:52
|In the '''Algebra view''' under '''Conic,''' click on the blue dot against '''c'''.

|-
|01:58
| We will draw three squares using the sides of the triangle.

|-
|02:02
| For that click on the '''Regular Polygon''' tool and then click on the points '''C''', '''B'''.

|-
|02:09
| The '''Regular Polygon''' text box opens with a default value 4.

|-
|02:14
|Click on '''OK''' button at the bottom.

|-
|02:17
| If you click on the points '''B''', '''C''', the square is drawn in the opposite direction.

|-
|02:25
| Let us undo the process by clicking on the '''Undo''' button.

|-
|02:29
| Now click on the points '''A''', C'''. And then click the '''OK''' button in the text box that appears.

|-
|02:37
| Similarly click on the points '''B''', '''A'''. And then click the '''OK''' button in the text box that appears.

|-
|02:46
| Now we have three squares that represent the '''Pythagorean triplets'''.

|-
|02:51
|Now we will use '''Zoom Out''' tool to see the diagram clearly.

|-
|02:57
| Now we will find the area of these squares.

|-
|03:01
| Click on the '''Area''' tool and click on '''poly1''', '''poly2''' and '''poly3''' respectively.

|-
|03:12
|The areas of the respective squares are displayed.

|-
|03:16
| Using the '''Move''' tool drag the labels to see them clearly.

|-
|03:29
|Now we will check if the area of '''poly1''' + area of '''poly 2''' is equal to area of '''poly3.'''

|-
|03:36
|In the '''input bar ''' type '''poly1+ poly2 ''' and press '''Enter'''.

|-
|03:43
|In the Algebra view a '''Number d''', shows the value of area of '''poly3'''.

|-
|03:49
| Hence '''Pythagoras''' theorem has been proved.

|-
|03:52
|Now I will explain the '''Construction Protocol''' for '''pythagoras''' theorem.

|-
|03:57
| '''Construction Protocol''' shows the step by step construction of the diagram as an animation.

|-
|04:03
| To view the animation, click on '''View''' menu and select '''Construction Protocol''' check box.

|-
|04:10
| '''Construction Protocol view''' opens next to '''Graphics view'''.

|-
| 04:15
| I will drag the boundary of Graphics view view to see the '''Construction Protocol view'''.

|-
|04:21
| This view has a table with some columns. Below the table we have the animation controls.

|-
|04:29
| Now click on the '''Play''' button.

|-
|04:32
| Watch the step by step construction of the figure as an animation.

|-
|04:50
| Now we will prove the Mid-point theorem.

|-
|04:53
|The line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it.

|-
|05:01
| I have opened a new '''GeoGebra''' window.

|-
|05:05
| Let us draw a triangle '''ABC''' using '''Polygon''' tool.

|-
| 05:16
| Now we will find the mid-points of the sides '''AB''' and '''AC'''.

|-
|05:21
| Click on the '''Midpoint or Center''' tool. Then click on the sides '''AB''' and '''AC'''.

|-
|05:30
|Using the '''Line''' tool, draw a line through points '''D''' and '''E'''.

|-
|05:38
|Now we will draw a line parallel to segment '''AB'''.

|-
|05:42
|For this, click on the '''Parallel Line''' tool and click on segment '''AB'''.

|-
|05:49
| Then, click on point '''C'''. Line '''g''' parallel to segment '''AB''' is drawn.

|-
|05:56
|Notice that lines '''f''' and '''g''' intersect at a point.

|-
|06:01
| Using the '''Intersect''' tool, let us mark the point of intersection as '''F'''.

|-
|06:08
| Now we need to measure angles '''F C E''' and '''D A E'''.

|-
|06:17
| Click on the '''Angle''' tool and click on the points '''F''', '''C''', '''E''' and '''D''', '''A''', '''E'''.

|-
|06:32
| Notice that angles are equal since they are alternate interior angles.

|-
|06:38
| Similarly we will measure '''C''', '''B''', '''D''' and '''E''', '''D''', '''A''' .

|-
|06:49
| The angles are equal. This implies that line '''f''' is parallel to segment '''BC'''.

|-
|06:56
| Using the '''Distance or Length''' tool, click on the points '''D''', '''E''' and '''B''', '''C'''.
Notice that '''DE''' is half of '''BC'''.

|-
|07:09
| Hence the mid-point theorem is proved.

|-
|07:12
| Once again I will show the '''Construction Protocol''' for the theorem.

|-
|07:17
| Click on '''View '''menu select '''Construction Protocol '''check box.

|-
| 07:23
|''Construction Protocol''' view opens next to '''Graphics view'''.

|-
|07:28
| Now click on the '''Play''' button.

Watch the step by step construction of the figure.

|-
|07:51
| As an assignment, prove this theorem.

|-
|07:55
| Your completed assignment should look like this.

|-
| 07:59
| Let us summarize what we have learnt.

|-
|08:02
| In this tutorial we stated and proved,

'''Pythagoras''' theorem and

Midpoint theorem using '''Geogebra'''

|-
|08:12
| The video at the following link summarizes the Spoken Tutorial project.
Please download and watch it.

|-
|08:20
|The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.
For more details, please write to us.

|-
|08:28
| Please post your timed queries in this forum.

|-
|08:32
| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
More information on this mission is available at this link.

|-
| 08:43
|This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching.

|-
|}

@@ Line 21: / Line 21: @@
 '''Ubuntu Linux''' OS version 16.04
-'''GeoGebra''' version 5.0438.0-d.
+'''GeoGebra''' version 5.0.438.0-d.
 |-

GeoGebra-5.04/C2/Theorems-in-GeoGebra/English-timed - Revision history

PoojaMoolya at 10:08, 10 October 2019

PoojaMoolya: Created page with "{| border = 1 || ''' Time''' || ''' Narration''' |- |00:01 |Welcome to the spoken tutorial on '''Theorems in GeoGebra'''. |- |00:06 |In this tutorial we will state and pr..."